QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations

TL;DR

This paper investigates QCD-like theories on a compactified space, demonstrating a smooth transition from Abelian confinement at small circle size to non-Abelian confinement at large size using double-trace deformations, enabling insights into QCD.

Contribution

It introduces a method to connect small and large circle regimes in QCD-like theories via double-trace deformations, preserving key features across the transition.

Findings

Calculated string tension, mass gap, and condensates at small circle size.

Showed the double-trace deformation becomes irrelevant at large circle size.

Established a continuous connection between Abelian and non-Abelian confinement regimes.

Abstract

We consider QCD-like theories with one massless fermion in various representations of the gauge group SU$(N)$. The theories are formulated on $R_3\times S_1$. In the decompactification limit of large $r(S_1)$ all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ($\chi$SB). At small $r(S_1)$, in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small $r(S_1)$ and yet exhibit basic features of the large-$r(S_1)$ limit: confinement and $\chi$SB. We calculate the string tension, mass gap, bifermion condensates and $\theta$ dependence. The double-trace deformation becomes dynamically irrelevant at large $r(S_1)$. Despite the fact that at small $r(S_1)$ confinement is Abelian, while it is expected to be non-Abelian at large $r(S_1)$, we argue that small and large-$r(S_1)$ physics are continuously connected. If so, one can use small-$r(S_1)$ laboratory to extract lessons about QCD and QCD-like theories on $R_4$.